Fuzzy methods for case-based recommendation and decision support

The paper proposes two case-based methods for recommending decisions to users on the basis of information stored in a database. In both approaches, fuzzy sets and related (approximate) reasoning techniques are used for modeling user preferences and decision principles in a flexible manner. The first approach, case-based decision making, can principally be seen as a case-based counterpart to classical decision principles well-known from statistical decision theory. The second approach, called case-based elicitation, combines aspects from flexible querying of databases and case-based prediction. Roughly, imagine a user who aims at choosing an optimal alternative among a given set of options. The preferences with respect to these alternatives are formalized in terms of flexible constraints, the expression of which refers to cases stored in a database. As both types of decision support might provide useful tools for recommender systems, we also place the methods in a broader context and discuss the role of fuzzy set theory in some related fields.     

Implementation of fuzzy classification in relational databases using conventional SQL querying

In this paper, a framework for implementing fuzzy classifications in information systems using conventional SQL querying is presented. The fuzzy classification and use of conventional SQL queries provide easy-to-use functionality for data extraction similar to the conventional non-fuzzy classification and SQL querying. The developed framework can be used as data mining tool in large information systems and easily integrated with conventional relational databases. The benefits of using the presented approach include more flexible data analysis and improvement of information presentation at the report generation phase. To confirm the theory, a prototype was developed based on the stored procedures and database extensions of Microsoft SQL Server 2000.     

Design and implementation of index structures for fuzzy spatial databases

Over the years database management systems have evolved to include spatially referenced data. Because spatial data are complex and have a number of unique constraints (i.e., spatial components and uncertain properties), spatial database systems can be effective only if the spatial data are properly handled at the physical level. Therefore, it is important to develop an effective spatial and aspatial indexing technique to facilitate flexible spatial and/or aspatial querying for such databases. For this purpose we introduce an indexing approach to use (fuzzy) spatial and (fuzzy) aspatial data. We use a number of spatial index structures, such as Multilevel Grid File (MLGF), G-tree, R-tree, and R^*-tree, for fuzzy spatial databases and compare the performances of these structures for various flexible queries. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 805–826, 2007.     

一种有效的估计关系数据库中空值的方法

由于客观世界的复杂性,信息缺失、不确定信息是普遍存在的。数据库作为表达现实世界的一种工具,使用空值来表达信息缺失的问题。针对关系数据库中的空值问题,提出一种基于模糊聚类和线性回归的空值估计方法。该方法首先对数据表中的数据进行挖掘,找出与被估计属性相关联的属性集。该过程仅利用数据本身提供的信息,避免了由专家决定条件属性时由于主观性造成的误差。其次根据所得属性集进行模糊聚类得到对原始数据的一个划分,再基于所得分簇和线性回归给出一个估计关系表中空值的方法。最后利用平均绝对错误率来衡量算法估值的准确率。实验结果表明该方法估值的结果与其他方法相比具有较高的准确率。     

ESTIMATING NULL VALUES IN THE DISTRIBUTED RELATIONAL DATABASES ENVIRONMENT

To estimate nullvalues in relational database systems is an important research topic. In Chen and Yeh (1997) a method for estimating null values in relational database systems was presented. In Chen and Chen (1997) a method for fuzzy query translation for information in the distributed relational databases environment was presented. In this article, the works of Chen and Chen (1997) and Chen and Yeh (1997) are extended to propose a method for estimating null values in the distributed relational databases environment. The proposed method provides a useful way to estimate incomplete data when the relations stored in a failed server cannot be accessed in the distributed relational databases environment.     

Generalization of strategies for fuzzy query translation in classical relational databases

Users of information systems would like to express flexible queries over the data possibly retrieving imperfect items when the perfect ones, which exactly match the selection conditions, are not available. Most commercial DBMSs are still based on the SQL for querying. Therefore, providing some flexibility to SQL can help users to improve their interaction with the systems without requiring them to learn a completely novel language. Based on the fuzzy set theory and the α-cut operation of fuzzy number, this paper presents the generic fuzzy queries against classical relational databases and develops the translation of the fuzzy queries. The generic fuzzy queries mean that the query condition consists of complex fuzzy terms as the operands and complex fuzzy relations as the operators in a fuzzy query. With different thresholds that the user chooses for the fuzzy query, the user’s fuzzy queries can be translated into precise queries for classical relational databases.     

基于Vague数据库的代数查询语言

基于Vague集理论的Vague关系数据库与其他模糊数据库一样,由于所含信息的模糊性,对应着现实世界的多种状态.虽然此类数据库能够更加真实地反映现实世界,但是在基于这些数据库的查询语言的有效性和计算过程的复杂性等方面却存在着一定的问题.本文基于Vague关系数据模型,对其代数查询语言中的选择、投影和连接操作进行了研究,指出基于一般Vague关系数据模型的查询语言中所存在的问题,并提出相应的解决方法,引入一种嵌套机制,对Vague关系模型进行了进一步扩展,进而对新模型查询语言中的三种操作在不同情况下进行了讨论,并给出了相应的定义.     

Fuzzy rough set techniques for uncertainty processing in a relational database

This paper concerns the modeling of imprecision, vagueness, and uncertainty in databases through an extension of the relational model of data: the fuzzy rough relational database, an approach which uses both fuzzy set and rough set theories for knowledge representation of imprecise data in a relational database model. The fuzzy rough relational database is formally defined, along with a fuzzy rough relational algebra for querying. Comparisons of theoretical properties of operators in this model with those in the standard relational model are discussed. An example application is used to illustrate other aspects of this model, including a fuzzy entity–relationship type diagram for database design, a fuzzy rough data definition language, and an SQL‐like query language supportive of the fuzzy rough relational database model. This example also illustrates the ease of use of the fuzzy rough relational database, which often produces results that are better than those of conventional databases since it more accurately models the uncertainty of real‐world enterprises than do conventional databases through the use of indiscernibility and fuzzy membership values. ©2000 John Wiley & Sons, Inc.     

Handling fuzzy information in extended possibility‐based fuzzy relational databases

Two kinds of fuzziness in attribute values of the fuzzy relational databases can be distinguished: One is that attribute values are possibility distributions, and the other is that there are resemblance relations in attribute domains. The fuzzy relational databases containing these two kinds of fuzziness simultaneously are called extended possibility‐based fuzzy relational databases. In this paper, we focus on such fuzzy relational databases. We classify two kinds of fuzzy data redundancies and define their removal. On this basis, we define fuzzy relational operations in relational algebra, which, being similar to the conventional relational databases, are complete and sound. In particular, we investigate fuzzy querying strategies and give the form of fuzzy querying with SQL. © 2002 Wiley Periodicals, Inc.     

A fuzzy knowledge-based system for intelligent retrieval

For many knowledge-intensive applications, it is important to develop an environment that permits flexible modeling and fuzzy querying of complex data and knowledge including uncertainty. With such an environment, one can have intelligent retrieval of information and knowledge, which has become a critical requirement for those applications. In this paper, we introduce a fuzzy knowledge-based (FKB) system along with the model and the inference mechanism. The inference mechanism is based on the extension of the Rete algorithm to handle fuzziness using a similarity-based approach. The proposed FKB system is used in the intelligent fuzzy object-oriented database (IFOOD) environment, in which a fuzzy object-oriented database is used to handle large scale of complex data while the FKB system is used to handle knowledge of the application domain. Both the fuzzy object-oriented database system and the fuzzy knowledge-based system are based on the object-oriented concepts to eliminate data type mismatches. The aim of this paper is mainly to introduce the FKB system of the IFOOD environment.     

On the primitivity of the division of fuzzy relations

 Allowing for flexible queries enables database users to express preferences inside elementary conditions and priorities between conditions. The division is one of the algebraic operators defined in order to query regular databases. This operation aims at the selection of A-elements which are connected with (at least) a given subset of B-elements, e.g., the stores which ordered all the items supplied by a given manufacturer. It is mainly used in the framework of the relational model of data, although it makes sense in object-oriented databases as well. In the relational context, the division is a non-primitive operation which may be expressed in terms of other operations, namely projection, Cartesian product and set difference. When fuzzy predicates appear, this operator needs to be extended to fuzzy relations and this requires the replacement of the usual implication by a fuzzy one. This paper proposes two types of meaning of the extended division and it investigates the issue of the primitivity of the extended operation (i.e., if the division of fuzzy relations is expressible in terms of other operations). The final objective is to decide whether this operator is necessary or not for the purpose of flexible querying and to help the design of a query language supporting flexible queries, among which those conveying a division of fuzzy relations.     

Functional dependencies with null values, fuzzy values, and crispvalues

Based on the concepts of the semantic proximity, we present a definition of the fuzzy functional dependency, We show that the inference rules for fuzzy functional dependencies, which are the same as Armstrong's axioms for the crisp case, are correct and complete. We also show that dependent constraints with dull values constitute a lattice. Functional dependencies in classical relational databases and null functional dependencies can be viewed as a special case of fuzzy functional dependencies. By applying the unified functional dependencies to the relational database design, we can represent the data with fuzzy values, null values and crisp values under relational database management systems, By using fuzzy functional dependencies, we can compress the range of a fuzzy value and make this fuzzy value “clearer”     

Algebraic operations in fuzzy object-oriented databases

The fuzzy object-oriented databases have been proposed to meet the need of dealing with fuzzy as well as complex objects. In this paper, we present a formal fuzzy object-oriented database model. Based on the semantic measure of fuzzy data, we first identify two kinds of fuzzy object redundancies, which are inclusion redundancy and equivalence redundancy, and then define three kinds of merging operation for redundancy removal. On the basis, we define some fuzzy algebraic operations for fuzzy classes and fuzzy objects. Finally, in the paper, we discuss fuzzy querying strategies and give the form of SQL-like fuzzy querying for the fuzzy object-oriented databases.     

Modeling and querying fuzzy spatiotemporal databases

Modeling spatiotemporal data, in particular fuzzy and complex spatial objects representing geographic entities and relations, is a topic of great importance in geographic information systems, computer vision, environmental data management systems, etc. Because of complex requirements, it is challenging to represent spatiotemporal data and its features in databases and to effectively query them. This article presents a new approach to model and query the spatiotemporal data of fuzzy spatial and complex objects and/or spatial relations. In our case study, we use a meteorological database application in an intelligent database architecture, which combines an object-oriented database with a knowledgebase for modeling and querying spatiotemporal objects.     

GENERATING FUZZY RULES FROM RELATIONAL DATABASE SYSTEMS FOR ESTIMATING NULL VALUES

This paper presents a new algorithm for constructing fuzzy decision trees from relational database systems and generating fuzzy rules from the constructed fuzzy decision trees. We also present a method for dealing with the completeness of the constructed fuzzy decision trees. Based on the generated fuzzyrules, we also present a method for estimating null values in relational database systems. The proposed methods provide a useful way to estimate null values in relational database systems.     

Bayesian networks for supporting query processing over incomplete autonomous databases

As the information available to naïve users through autonomous data sources continues to increase, mediators become important to ensure that the wealth of information available is tapped effectively. A key challenge that these information mediators need to handle is the varying levels of incompleteness in the underlying databases in terms of missing attribute values. Existing approaches such as QPIAD aim to mine and use Approximate Functional Dependencies (AFDs) to predict and retrieve relevant incomplete tuples. These approaches make independence assumptions about missing values—which critically hobbles their performance when there are tuples containing missing values for multiple correlated attributes. In this paper, we present a principled probabilistic alternative that views an incomplete tuple as defining a distribution over the complete tuples that it stands for. We learn this distribution in terms of Bayesian networks. Our approach involves mining/“learning” Bayesian networks from a sample of the database, and using it to do both imputation (predict a missing value) and query rewriting (retrieve relevant results with incompleteness on the query-constrained attributes, when the data sources are autonomous). We present empirical studies to demonstrate that (i) at higher levels of incompleteness, when multiple attribute values are missing, Bayesian networks do provide a significantly higher classification accuracy and (ii) the relevant possible answers retrieved by the queries reformulated using Bayesian networks provide higher precision and recall than AFDs while keeping query processing costs manageable.     

An efficient method for estimating null values in relational databases

Generally, a database system containing null value attributes will not operate properly. This study proposes an efficient and systematic approach for estimating null values in a relational database which utilizes clustering algorithms to cluster data, and a regression coefficient to determine the degree of influence between different attributes. Two databases are used to verify the proposed method: (1) Human resource database; and (2) Waugh's database. Furthermore, the mean of absolute error rate (MAER) and average error are used as evaluation criteria to compare the proposed method with other methods. It demonstrates that the proposed method is superior to existing methods for estimating null values in relational database systems. Jia-Wen Wang was born on September 5, 1978, in Taipei, Taiwan, Republic of China. She received the M.S. degree in information management from the National Yunlin University of Science and Technology, Yunlin, Taiwan, in 2003. Since 2003, she has been a PhD degree student in Information Management Department at the National Yunlin University of Science and Technology. Her current research interests include fuzzy systems, database systems, and artificial intelligence. Ching-Hsue Cheng received the B.S. degree in mathematics from Chinese Military Academy, Taiwan, in 1982, the M.S. degree in applied mathematics from the Chung Yuan Christian University, Taiwan, in 1988, and the Ph.D. degree in system engineering and management from National Defence University, Taiwan, in 1994. Currently, he is a professor of the Department of Information Management, National YunLin University of Technology & Science. His research interests are in decision science, soft computing, software reliability, performance evaluation, and fuzzy time series. He has published more than 120 refereed papers in these areas. He has been a principal investigator and project leader in a number of projects with government, and other research-sponsoring agencies.     

FILIP: A fuzzy intelligent information system with learning capabilities

FILIP (fuzzy intelligent learning information processing) system is designed with the goal to model human information processing. The issues addressed are uncertain knowledge representation and approximate reasoning based on fuzzy set theory, and knowledge acquisition by “being told” or by “learning from examples”. Concepts that can be “learned” by the system can be imprecise (fuzzy), or the knowledge can be incomplete. In the latter case, FILIP uses the concept of similarity to extrapolate the knowledge to cases that were not covered by examples provided by the user. Concepts are stored in the Knowledge Base and employed in intelligent query processing, based on flexible inference that supports approximate matches between the data in the database and the query.

The architecture of FILIP is discussed, the learning algorithm is described, and examples of the system's performance in the knowledge acquisition and querying modes, together with its explanatory capabilities are shown.     

基于多表关联的关系数据库多空值估计方法

由于客观世界的复杂性,信息缺失、不确定是普遍存在的。数据库作为表达现实世界的一种工具,使用空值来表达信息缺失的现象。针对关系数据库中的空值问题,提出一种基于多表关联的多空值估计方法。该方法首先以尽可能少地引入误差的原则确定估计每一列空值的顺序;然后对每一列空值先采用本表的信息进行估计,当预测误差大于给定阈值时,根据该表与其他表的关系形式选择不同的模式引入多表信息来提高预测的准确度。实验结果表明该方法估计空值的效果与其他方法相比有较高的准确率。      

Storing and querying fuzzy XML data in relational databases

Information imprecision and uncertainty exist in many real-world applications and for this reason fuzzy data management has been extensively investigated in various database management systems. Currently, introducing native support for XML data in relational database management systems (RDBMs) has attracted considerable interest with a view to leveraging the powerful and reliable data management services provided by RDBMs. Although there is a rich literature on XML-to-relational storage, none of the existing solutions satisfactorily addresses the problem of storing fuzzy XML data in RDBMs. In this paper, we study the methodology of storing and querying fuzzy XML data in relational databases. In particular, we present an edge-based approach to shred fuzzy XML data into relational data. The unique feature of our approach is that no schema information is required for our data storage. On this basis, we present a generic approach to translate path expression queries into SQL for processing XML queries.